Clearly \(\kappa (c)\le \kappa \)  and \(\kappa (c)\)  takes into account both
the spectrum and the magnitude of solution components across eigenspaces. It
is also known, e.g. [1]}, that the relative error in approximations is
bounded by \(\kappa (c)\)  times the relative residual. To our knowledge, this
extension is due to Chan and Foulser [2]}. It was soon thereafter
developed by Axelsson [3]}, [1]} and has been further developed
in important work in [5]}, [6]}, [7]}, [8]}, [9]}, [10]}.
